Stochastic Model Predictive Control of constrained linear systems with additive uncertainty

This paper illustrates a stochastic Model Predictive Control (MPC) algorithm to control a linear system subject to additive zero-mean noise, state and input constraints. The algorithm proposed is computationally efficient since it can be formulated as a SemiDefinite Programming (SDP) problem and can thus be solved by interior-point methods. We also show that, under the hypotesis of bounded noise, the closed-loop system can be rendered Input-to-State-Stable (ISS).